Enhancement of anomalous boundary current by high temperature

Recently it is found that Weyl anomaly leads to novel anomalous currents in the spacetime with a boundary. However, the anomalous current is suppressed by the mass of charge carriers and the distance to the boundary, which makes it difficult to be measured. In this paper, we explore the possible mechanisms for the enhancement of anomalous currents. Interestingly, we find that the anomalous current can be significantly enhanced by the high temperature, which makes easier the experimental detection. For free theories, the anomalous current is proportional to the temperature in the high temperature limit. Note that the currents can be enhanced by thermal effects only at high temperatures. In general, this is not the case at low temperatures. For general temperatures, the absolute value of the current of Neumann boundary condition first decreases and then increases with the temperature, while the current of Dirichlet boundary condition always increases with the temperature. It should be mentioned that the enhancement does not have an anomalous nature. In fact, the so-called anomalous current in this paper is not always related to Weyl anomaly. Instead, it is an anomalous effect due to the boundary.

Event boundary detection using autonomous agents in a sensor network

We propose a novel approach to event boundary detection, where autonomous agents are deployed in order to minimize the number of transmissions required to discover an event boundary. The goal of our algorithm is to reduce the number of non-boundary node transmissions (i.e. nodes within the event area and not within transmission distance to the boundary), since the sensory data from these nodes are not required for event boundary detection. The algorithm works by first randomly generating a fraction of agents within the event nodes, then discovering and mapping the boundary, and finally reporting the aggregated results to the user. Simulations demonstrate that the algorithm exhibits O(n) efficiency relationship with the event area, which is an improvement over existing methods that show O(n²) relationships. Furthermore, we demonstrate that the boundary of an event may be successfully mapped using the proposed algorithm.

Event boundary detection using autonomous agents in a sensor network

We propose a novel approach to event boundary detection, where autonomous agents are deployed in order to minimize the number of transmissions required to discover an event boundary. The goal of our algorithm is to reduce the number of non-boundary node transmissions (i.e. nodes within the event area and not within transmission distance to the boundary), since the sensory data from these nodes are not required for event boundary detection. The algorithm works by first randomly generating a fraction of agents within the event nodes, then discovering and mapping the boundary, and finally reporting the aggregated results to the user. Simulations demonstrate that the algorithm exhibits O(n) efficiency relationship with the event area, which is an improvement over existing methods that show O(n²) relationships. Furthermore, we demonstrate that the boundary of an event may be successfully mapped using the proposed algorithm.

On the behavior of 1-Laplacian ratio cuts on nearly rectangular domains

The $p$-Laplacian has attracted more and more attention in data analysis disciplines in the past decade. However, there is still a knowledge gap about its behavior, which limits its practical application. In this paper, we are interested in its iterative behavior in domains contained in two-dimensional Euclidean space. Given a connected set $\varOmega _0 \subset \mathbb{R}^2$, define a sequence of sets $(\varOmega _n)_{n=0}^{\infty }$ where $\varOmega _{n+1}$ is the subset of $\varOmega _n$ where the first eigenfunction of the (properly normalized) Neumann $p$-Laplacian $ -\varDelta ^{(p)} \phi = \lambda _1 |\phi |^{p-2} \phi $ is positive (or negative). For $p=1$, this is also referred to as the ratio cut of the domain. We conjecture that these sets converge to the set of rectangles with eccentricity bounded by 2 in the Gromov–Hausdorff distance as long as they have a certain distance to the boundary $\partial \varOmega _0$. We establish some aspects of this conjecture for $p=1$ where we prove that (1) the 1-Laplacian spectral cut of domains sufficiently close to rectangles is a circular arc that is closer to flat than the original domain (leading eventually to quadrilaterals) and (2) quadrilaterals close to a rectangle of aspect ratio $2$ stay close to quadrilaterals and move closer to rectangles in a suitable metric. We also discuss some numerical aspects and pose many open questions.

Geometric Hardy and Hardy–Sobolev inequalities on Heisenberg groups

In this paper, we present geometric Hardy inequalities for the sub-Laplacian in half-spaces of stratified groups. As a consequence, we obtain the following geometric Hardy inequality in a half-space of the Heisenberg group with a sharp constant: [Formula: see text] which solves a conjecture in the paper [S. Larson, Geometric Hardy inequalities for the sub-elliptic Laplacian on convex domain in the Heisenberg group, Bull. Math. Sci. 6 (2016) 335–352]. Here, [Formula: see text] is the angle function. Also, we obtain a version of the Hardy–Sobolev inequality in a half-space of the Heisenberg group: [Formula: see text] where [Formula: see text] is the Euclidean distance to the boundary, [Formula: see text], and [Formula: see text]. For [Formula: see text], this gives the Hardy–Sobolev–Maz’ya inequality on the Heisenberg group.

Some Algorithms to Solve a Bi-Objectives Problem for Team Selection

In real life, many problems are instances of combinatorial optimization. Cross-functional team selection is one of the typical issues. The decision-maker has to select solutions among ( k h ) solutions in the decision space, where k is the number of all candidates, and h is the number of members in the selected team. This paper is our continuing work since 2018; here, we introduce the completed version of the Min Distance to the Boundary model (MDSB) that allows access to both the “deep” and “wide” aspects of the selected team. The compromise programming approach enables decision-makers to ignore the parameters in the decision-making process. Instead, they point to the one scenario they expect. The aim of model construction focuses on finding the solution that matched the most to the expectation. We develop two algorithms: one is the genetic algorithm and another based on the philosophy of DC programming (DC) and its algorithm (DCA) to find the optimal solution. We also compared the introduced algorithms with the MIQP-CPLEX search algorithm to show their effectiveness.

Weighted Sobolev regularity and rate of approximation of the obstacle problem for the integral fractional Laplacian

We obtain regularity results in weighted Sobolev spaces for the solution of the obstacle problem for the integral fractional Laplacian [Formula: see text] in a Lipschitz bounded domain [Formula: see text] satisfying the exterior ball condition. The weight is a power of the distance to the boundary [Formula: see text] of [Formula: see text] that accounts for the singular boundary behavior of the solution for any [Formula: see text]. These bounds then serve us as a guide in the design and analysis of a finite element scheme over graded meshes for any dimension [Formula: see text], which is optimal for [Formula: see text].

A geometrical version of Hardy-Rellich type inequalities

We obtained a version of Hardy-Rellich type inequality in a domain Ω ∈ ℝn which involves the distance to the boundary, the diameter and the volume of Ω. Weight functions in the inequalities depend on the “mean-distance” function and on the distance function to the boundary of Ω. The proved inequalities connect function to first and second order derivatives.

Development of a directional resistivity logging-while-drilling tool using a joint-coil antenna and its geosteering applications

Geosteering is a key technique to increase oil- and gas-production rates, especially within a thin reservoir layer. The purpose of geosteering in the production zone is to keep the drilling path in oil- and gas-bearing reservoirs. To keep the drilling system inside the production zone, downhole sensors must be able to detect bed boundaries, which include identifying the boundary location with respect to the sensor and the boundary distance from the sensor. We have developed a directional resistivity logging-while-drilling (LWD) tool for geosteering applications. The directional LWD tool is equipped with a joint-coil antenna composed of an axially polarized coil Rz connected in series with two transversely polarized coils Rx. During a revolution around the axis of the tool, the voltage of the axial coil VRz, voltage of the transverse coils VRx, and tool face angle [Formula: see text], which indicates the boundary direction, can be extracted through curve fitting the total voltage response of the joint-coil antenna. The distance to the boundary can be derived from a 1D inversion. The LWD tool has been tested in several reservoirs in China, and it has a demonstrated capability to provide reliable and accurate estimations of the boundary direction and distance. Field data indicate that the boundary detection depth can reach 2.1 and 1.7 m when the tool is in a sand and shale formation. Using wireline-logging data from surrounding wells as reference, deviations between the reference and the measured distance to the boundary are within 0.2 m.